The on line detection of engine misfire at low speed using multiple feature fusion with fuzzy pattern recognition

The on-line detection of engine misŽ re at low speed

using multiple feature fusion with fuzzy pattern

recognition

S Liu1*, F Gu2andA Ball2

1School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, People’s Republic of China

2Maintenance Engineering Research Group, School of Engineering, University of Manchester, Manchester, UK

Abstract: This paper proposes a technique for the on-line detection of incipient engine misŽ re based on multiple feature fusion and fuzzy pattern recognition. The technique requires the measurement of instantaneous angular velocity signals. By processing the engine dynamics model equation in the angular frequency domain, four dimensionless features for misŽ re detection are deŽ ned, along with fast feature-extracting algorithms. By directly analysing the waveforms of the angular velocity and the angular acceleration, six other dimensionless features are extracted. Via fuzzy pattern recognition, all the features are associated together as a fuzzy vector. This vector identiŽ es whether the engine is healthy or faulty and then locates the position of a misŽ ring cylinder or cylinders if necessary. The experimental work conducted on a production engine operating at low speeds conŽ rms that such a technique is able to work with the redundant and complementary information of all the features and that it leads to improved diagnostic reliability. It is fully expected that this technique will be simple to implement and will provide a useful practical tool for the on-line monitoring and real-time diagnosis of engine misŽ re in individual cylinders.

Keywords: internal combustion engine, condition monitoring, fault diagnosis, fuzzy pattern recognition, data fusion, misŽ re, angular velocity

I(_Fn) acceleration  uctuation index ofnth

NOTATION

cylinder

I(_Hn) maximum acceleration index ofnth a_m,b_m mth element of AandB

cylinder A¯(n) estimate of angular acceleration

I(_Ln) minimum acceleration index ofnth  uctuation of nth cylinder

cylinder A,B fuzzy vector

I(_Sn) summed acceleration index of nth c_m,d_m constant

cylinder DFT discrete Fourier transform

I(_Tn) torque  uctuation index ofnth cylinder h(õ) impulse response function of engine

I(_Vn) velocity variation index of nth cylinder dynamics model

J moment of inertia

H(ì) Fourier transform ofh(õ)

K number of frequency harmonics utilized

i = ­ 1

L number of data samples per engine cycle I(_An) acceleration variation index ofnth

M dimension ofAandB

cylinder

n cylinder number

I(_Cn) angular variation index ofnth cylinder

N number of cylinders

R_F acceleration component ratio R_T torque component ratio The MS was received on 29 June 2001 and was accepted after revision R_T,0 threshold forR_T

for publication on 30 January 2002. _{t time}

* Corresponding author: School of Mechanical Science and Engineering,

T_e(õ) rotating inertia torque Huazhong University of Science and Technology, Wuhan, Hubei,

T_L(õ) total resistive torque 1 INTRODUCTION T_L(ì) Fourier transform ofT_L(õ)

T_p(mì_c) DFT ofT_p(õ) at mì_c, for T_p(õ) within Considerable interest has been shown in the detection of one engine cycle incipient engine misŽ re in recent years. As exhaust emis-T(_pn)(mì_f) DFT ofT_p(õ) at mì_f, forT_p(õ) ofnth sion control regulations become increasingly stringent, cylinder within one engine cycle it becomes even more likely that, if possible, misŽ re will T_p(õ) gas pressure torque be monitored continuously by the on-board diagnostic T_p(ì) Fourier transform ofT_p(õ) system. To avoid costly engine failures and to reduce T¯(_pn) estimate of gas pressure torque output of repair time, the diagnostic system should also be capable

nth cylinder of indicating the fault location, i.e. identifying the

T_r(õ) reciprocating inertia torque misŽ ring cylinder or cylinders in an early stage. T_r(ì) Fourier transform ofT_r(õ) MisŽ re in internal combustion engines refers to a

situ-u_m mth element of U ation where the fuel–air mixture cannot be eYciently

U real vector _{combusted in one or more cylinders. Although direct}

x(õ) =[ö(õ)]2 _{measurement of in-cylinder pressure of each individual}

X(mì_c) DFT ofx(õ) atmì_c, for x(õ) within one _{cylinder may be the most precise approach for misŽ re} engine cycle _{detection, it is obviously impractical because it requires} X(n)(mì_f) DFT ofx(õ) atmì_f, forx(õ) of nth _{installing a costly pressure transducer in each cylinder.} cylinder within one engine cycle _{However, the instantaneous angular velocity can be} X(ì) Fourier transform ofx(õ) _{obtained easily and reliably, and this kind of signal may} be widely utilized for engine monitoring, diagnosis and á(õ) crankshaft angular acceleration

control [1–4]. á(_maxn) peak value of angular acceleration ofnth

The detection of engine misŽ re by instantaneous

angu-cylinder _{lar velocity measurement can be performed in two ways.}

á(_minn) valley value of angular acceleration of

The Ž rst is based on waveform analysis, in which the nth cylinder

instantaneous velocity waveform is analysed directly and á(_sumn) summed absolute value of angular

the extracted feature used to identify whether misŽ re acceleration of nth cylinder

exists in the engine by simple threshold or by more com-å minor positive value quite near zero

plicated Bayesian decision theory [5–7]. The second is õ crankshaft angular position

based on torque estimation, in which the instantaneous õ(_maxn) crankshaft angular position

gas pressure torque (indicated torque) or individual cyl-corresponding to ö(_maxn)

inder pressure is calculated by an engine dynamics õ(_minn) crankshaft angular position

model, and from this the misŽ ring cylinder is identiŽ ed corresponding to ö(_minn)

[8–17]. ¢õ_(n) crankshaft angular duration

At present, almost all misŽ re detection techniques are corresponding to ¢ö_(n)

based only on a single feature or indicator. Each tech-[¢õ](n) crankshaft angular interval

nique has its own advantages and drawbacks with the corresponding to nth cylinder

result that no single technique has proven to be com-ì angular frequency variable

pletely reliable over a range of operating conditions. An ì_c engine cycle frequency

important consideration is that under complex con-ì_f engine Ž ring frequency

ditions (such as when misŽ re happens simultaneously in í fuzziŽ cation member function

multiple cylinders) the information required to make ó degree of closeness between two fuzzy

reliable misŽ re decisions may simply not be available vectors

in a single feature. The diagnostic conclusions drawn ó₁ maximum–minimum degree of closeness

by diVerent single features do not always concur and ó₂ Euclidean distance degree of closeness

sometimes directly con ict [7,16]. ó₀ threshold foró₁(or ó₂)

In recent years, multisensor data fusion has received ö(õ) crankshaft angular velocity

signiŽ cant attention for automated target recognition, ö

k ö_{engine cycle}(õ) sampled at point kwithin one _{guidance for autonomous vehicles, remote sensing,} battle-Ž eld surveillance, monitoring of manufacturing ö(_n)

k ö_{within one engine cycle}(õ) sampled at point kof nth cylinder _{process, condition-based maintenance of complex} machinery, robotics and medical applications [18–20]. ö(_maxn) peak value of angular velocity ofnth

Data fusion techniques combine data from diVerent sen-cylinder

sors with related information from an associated data-ö(_minn) value of angular velocity of nth

base to achieve improved accuracy and more speciŽ c cylinder

of sensitivity in one sensor domain can be oVset by infor- acceleration is actually an inverse problem, which can be solved more easily by transforming equation (1) from mation from other sensors, enabling, in theory,

success-ful decision-making ability over a wider range of the angular time domain to the angular frequency domain:

operating conditions.

In this paper, a technique for the on-line detection of

T_p(ì)=T_e(ì)+T_r(ì)+T_L(ì) engine misŽ re, which employs information from multiple

features, is proposed. The remainder of the paper is ₌1

2iìX(ì)[H(ì)]Õ 1+Tr(ì)+TL(ì) (2) organized as follows. In section 2, 10 dimensionless

fea-whereìis the variable in the angular frequency domain tures for misŽ re detection are introduced, along with fast

corresponding to the variableõin the crankshaft angular extraction algorithms. In section 3, the architecture for

domain, T_p(ì), T_e(ì), T_r(ì) and T_L(ì) are the Fourier the on-line misŽ re detection by multiple feature fusion

transforms of T_p(õ), T_e(õ), T_r(õ) and T_L(õ) respect-is presented. The multiple feature fusion procedure respect-is

ively,H(ì) is the Fourier transform ofh(õ) acting as the described in section 4. In section 5, the technique is

dem-transfer function of the system, X(ì) is the Fourier onstrated on experimental data from a four-cylinder

transform of x(õ)=[ö(õ)]2 and i= ­ 1. Note that four-stroke diesel engine. This study is concluded in

the equality T_e(ì)=1₂iìX(ì)[H(ì)]Õ 1 is obtained from section 6.

the diVerentiation property of Fourier transform, i.e. the Fourier transform of dx(õ)/dõis iìX(ì), and the relation-ship between angular acceleration and angular velocity

2 DIMENSIONLESS FEATURES AND

in theõdomain:

EXTRACTION ALGORITHMS

á(õ)=á(t)=dö_dt(t)=dö_d[õ_t(t)]=dö_dõ(õ)dõ_d(_tt)

2.1 Engine dynamics model and gas pressure torque estimation

=dö_d(_õõ)ö(õ)=1₂ d[ö_d(_õõ)]2=1₂dx_d(_õõ) (3) If it is assumed that the engine is operating in a steady

state condition and the crankshaft system is rigid, the

In equation (2), both T_r(ì) and T_L(ì) can be pre-non-linear engine dynamics model is based on the

calculated becauseT_r(õ) is purely deterministic and com-familiar torque balance equation [12–16]

pletely described by engine geometry and T_L(õ) is Jõ¨_=T

e(õ)=Tp(õ)­ Tr(õ)­ TL(õ) (1) assumed constant. Therefore, once a data block ofö(õ), sampled at discrete evenly spaced crankshaft intervals whereJis the eVective moment of inertia of the rotating

or sampled in the õ domain, is obtained, X(ì) will be parts of the engine,õrepresents the crankshaft angular

directly computed by the discrete Fourier transform position and is hence a function of timet, i.e. õ=õ(t),

(DFT) of the square of this data block, giving an õÇ_=dõ/dt, õ¨=d2õ/dt2,T_e(õ) andT_r(õ) are the rotating

estimate of gas pressure torque T_p(ì) in theì domain. inertia torque (or net torque) and the reciprocating

iner-tia torque associated with the ineriner-tia of rotating and reciprocating components respectively, T_p(õ) is the gas

pressure torque (or indicated torque) due to the force _{2.2 Feature extraction based on gas pressure torque} generated by the combustion pressure andT_L(õ) is the _estimation

total resistive torque of the engine.

Equation (1) can be further derived to a second-order There are two methods that can be used to calculate T_p(ì) in the ì domain by equation (3), which lead to non-linear diVerential equation [14], which reveals

explicitly the relationship between the cylinder pressure the development of diVerent fast algorithms of feature extraction for engine misŽ re detection. The Ž rst method and the instantaneous crankshaft angular velocity

ö(õ)=õÇ, and thus it is possible in theory to estimate is performed at harmonics of the engine cycle frequency, denoted by ì_c, providing a set of components ofT_p(ì) the cylinder pressure or gas pressure torque from the

measurements of ö(õ). In practice, however, it is quite for each engine cycle, and thus the calculation is based on the entire data block in each engine cycle. If the diYcult to solve such a complex equation directly in the

time domain. As shown in equation (1), the engine can engine runs normally with cylinder-to-cylinder uniform-ity, the component ofT_p(ì) corresponding to the Ž ring be treated as a dynamic system, of which the input is

the rotating inertia torque T_e(õ) and the output is the frequency is much larger in amplitude than those below the Ž ring frequency. However, if cylinder-to-cylinder angular accelerationá(õ)=õ¨. For a more general

situ-ation, supposing h(õ) to be the impulse response func- non-uniformity (e.g. misŽ re) happens in the engine, the harmonic components of T_p(ì) below the Ž ring fre-tion of the dynamic system, its outputá(õ) will be given

in convolution form á(õ)=T_e(õ)1h(õ). Therefore, the quency will increase signiŽ cantly. Because this property has been noticed, a dimensionless feature to detect mis-estimation of the gas pressure torque (or, furthermore,

the torque component ratio: engine cycle. Then, according to equations (2), (5) and (6), the calculation of the feature I(n)_T only requires K components of X(ì) at lower frequency harmonics for thenth cylinder in an engine cycle, which can be achieved R_T=

S

æ

NÕ ₁ m=₁|

T_p(mì_c)|2

|T_p(Nì_c)| (4) quickly by DFT:

whereNis the number of engine cylinders andT_p(mì_c)

X(n)(mì_f)= æMÕ 1 k=₀ [

ö_(n)

k ]2eÕ i2ðmk/M, m=1, 2, ...,K represents the gas pressure torque component at themth

harmonic within each engine cycle. ₍₈₎

The second method forT_p(ì) calculation is performed

at harmonics of the engine Ž ring frequency, denoted by _{The calculation of the features R}

T and I(n)T requires ì_f, giving a set of components ofT_p(ì) for each cylinder _{knowledge of the engine transfer function X(ì) that is} within each engine cycle, and thus the calculation is _{determined by the engine structural parameters.} made from each data block corresponding to each indi- _{However, it is usually not easy to obtain such structural} vidual cylinder. As the cylinder-to-cylinder  uctuation _{parameters for some engines. In this case, by neglecting} of the gas pressure torque indicates the power generation

the in uence of the reciprocating torque components capability of each individual cylinder, the torque output

T_r(ì) and by considering A(ì) as the estimate of T_p(ì), of each cylinder will be almost equal if the engine runs

two other similar dimensionless features have been under a normal cylinder-to-cylinder uniform condition.

deŽ ned for engine misŽ re detection: acceleration compo-Nevertheless, if misŽ re happens in a certain cylinder, the _{nent ratio,R}

F, and acceleration  uctuation index,I(n)F : torque output of this cylinder will decrease signiŽ cantly.

For this reason, another dimensionless feature to detect misŽ re for thenth individual cylinder has been deŽ ned and it is called the torque  uctuation index:

R_F=

S

æ

NÕ ₁ n=₁|A(n

ì_c)|2

|A(Nì_c)| (9)

I(n)_T= T¯(n)p 1 N æ

N n=₁T

¯_(n) p

(5)

I_(n)F = ₁ A¯(n)

N æ

N n=₁A

¯_(n) (10)

where T¯(n)_p is a parameter re ecting the gas pressure torque output of thenth cylinder, and it can be estimated

from the root mean square (r.m.s.) value of the lower _whereA(nì

c) represents the angular acceleration

compo-frequency components, i.e. _{nent at the nth frequency harmonic nì}

c within each engine cycle andA¯(n)is an estimate re ecting the angular T¯(n)_p =_K1

S

m=₁|T ¯_(n)

p (mìf)|2 (6) acceleration  uctuation of thenth cylinder. whereT(n)_p (mì_f) represents the gas pressure torque

com-ponent at the mth frequency harmonic mì_f for thenth cylinder within each engine cycle and Kis the number

of harmonics of ì_futilized. Kcan be determined using _{2.3 Feature extraction based on waveform analysis} knowledge of the combustion pressure as it propagates

According to equation (3), the instantaneous angular through the engine dynamics to cause angular velocity

acceleration á(õ) can be easily calculated from the  uctuations. For example, if the assumption is made that

measurements of instantaneous angular velocity ö(õ). most of the energy in the  uctuating gas pressure torque

Figure 1 depicts the waveforms ofá(õ) andö(õ) meas-is contained in the Ž rst three harmonics of ì_f, then

ured from a four-cylinder four-stroke diesel engine (see K=3 is suYcient to estimateT¯(n)_p.

Table 1) with cylinder 3 misŽ ring and Ž ltered by the fast LetLbe the number of angular velocity samples per

Fourier transform Ž ltering method. engine cycle and{ö

k:k=0, 1, 2, ...,L­ 1} be the data _{As previously discussed, á(õ) is proportional to the} block of angular velocity samples per engine cycle. Then,

engine rotating torqueT_e(õ). Thusá(õ) would be pro-according to equations (2) and (4), the calculation of

portional to the  uctuating component of the gas press-the feature R_T only requires N components of X(ì) at

ure torque T_p(õ) if the in uences of the reciprocating lower frequency harmonics within one engine cycle,

torque T_r(õ) and the resistive torque T_L(õ) were to be which can be obtained quickly by DFT:

neglected. This helps directly to deŽ ne three dimen-sionless features from the angular acceleration waveform X(mì_c)= æLÕ 1

k=₀

ö_2keÕ i2ð_{mk/L, m=1, 2, ...,N (7)}

for the misŽ re detection of an individual cylinder. These have been called the maximum acceleration index, Let{ö_nk:k=0, 1, 2, ...,L/N­ 1;n=1, 2, ...,N}be the

angular positions. Then, the maximum variation in the instantaneous angular velocity, ¢ö(n)=ö_(n)max­ ö_(n)min, and its corresponding angular duration, ¢õ_(n)=õ_(n)max­ õ_(n)min, are both indicators of the mean gas pressure torque of thenth cylinder. Therefore, three fea-tures can be deŽ ned to identify whether thenth cylinder is misŽ ring. They are called the angular variation index I(n)_C , velocity variation index, I(n)_V and acceleration vari-ation index,I(n)_A :

I_(n)C = ₁ ¢õ(n)

N æ

N n=₁

¢õ_(n)

(14)

I(n)_V= ₁ ¢ö(n)

N æ

N n=₁

¢ö_(n)

(15)

Fig. 1 Waveforms of (a) instantaneous angular acceleration and (b) instantaneous angular velocity during a cycle in a four-cylinder four-stroke engine

I(n)_A=

¢ö_(n) ¢õ_(n) 1 N æN

n=₁ ¢ö_(n) ¢õ_(n)

(16) Table 1 SpeciŽ cation of the test engine

Engine type Model 4135D, 8.6 l, 4-cylinder, 4-stroke, direct injection diesel

Manufacturer Shanghai Diesel Works _{3 ON-LINE MISFIRE DETECTION BY}

Bore×stroke 135 mm×150 mm

Maximum power output 123.6 kW at 1500 r/min MULTIPLE FEATURE FUSION Maximum torque 582 N m at 1200 r/min

Compression ratio 17:1

3.1 MisŽ re detection by each individual feature

Firing order 1–3–4–2 (from timing cover)

So far 10 dimensionless features have been deŽ ned along with fast feature extraction algorithms. Here rules are acceleration index, I(n)_S :

presented for each individual feature to identify engine misŽ re. Among these rules, rule 1 is forR_T andR_F and I_(n)H=₁ á(n)max

N æ

N n=₁

á_(n)max

(11) _{rules 2–4 are for I(n)}

T , I(n)F , I(n)H, I(n)L , I(n)S , I(n)C , I(n)V and

I(n)_A .

TakingR_Tas an example, rule 1 for a selected thresh-oldR_T,0would be

I(n)_L=₁ á(n)min

N æ

N n=₁

á_(n)min

(12)

Rule 1

IFR_Tå R_T,0

THEN all cylinders are healthy

ELSE one or more cylinders is misŽ ring I_(n)S =₁ á(n)sum

N æ

N n=₁

á_(n)sum

=

P

|á(õ)|dõ

1 N æ

N

n=₁

P

á(õ)|dõ

(13)

TakingI(n)_T as an example, rules 2–4 for a selected value åare as follows. Here åis a minor positive value quite near zero. Its introduction is to distinguish the normally where á_(n)max, á_(n)min and á_(n)sum are respectively the peak

acceptable cylinder-to-cylinder non-uniformity from the value, the valley value and the summed absolute value

abnormal misŽ re and thus to avoid a mistaken diagnosis. of the angular acceleration waveform of thenth cylinder

and [¢õ](n)is the crankshaft angular interval

correspond-Rule 2 ing to thenth cylinder.

As shown in Fig. 1b, in the waveform of instantaneous _{IF 1}

­ åå I(n)_T å 1+åfor all cylinders angular velocity there exists an acceleration during the _{THEN all cylinders are healthy} expansion stroke of each cylinder because of the

combus-tion pressure force. Let ö(n)_max and ö(n)_min be respectively _{Rule 3} the peak value and valley value of the angular velocity

waveform during the expansion stroke of thenth cylin- IFI_(n)T <1­ å

Rule 4

IFI_(n)T >1+å

Then thenth cylinder is healthy while misŽ re exists in another cylinder or cylinders

3.2 On-line misŽ re detection by multiple feature fusion

According to rule 1, among the 10 dimensionless fea-tures, neither R_T nor R_F is capable of identifying the misŽ ring cylinder(s), but both of them can detect

Fig. 3 Proposed architecture of multiple feature fusion whether the engine is healthy or faulty with much simpler

computations. According to rules 2–4, on the contrary,

single sensor provides the data (i.e. the instantaneous all of the other eight features have the capability to

ident-angular velocity signal ), from which several single ify the individual misŽ ring cylinder(s) but with more

features are extracted by diVerent feature extraction complex computations. For this reason, a technique for

approaches. Then these features are associated together the on-line detection of engine misŽ re has been proposed

into a single feature vector, which in turn is input to a which aims at achieving improved diagnostic eYciency

decision-making procedure, which may be a neural net-and reliability.

work or clustering algorithm. Noticing that the decision The technique is depicted in Fig. 2, where all of the _{making is in fact a process of pattern recognition; here} 10 dimensionless features are used. If the engine

struc-a fuzzy pstruc-attern recognition technique [21] is introduced, tural parameters are known,R_Twill identify whether the

which is particularly suitable for the association of engine is healthy or faulty at Ž rst andI(n)_T will then locate

multiple dimensionless features. The principles are the position of a misŽ ring cylinder or cylinders if

neces-demonstrated in the following section. sary. Otherwise, if the engine structural parameters are

unknown, R_F will detect whether the engine is healthy,

and the remaining seven features can then be used to _{4 MULTIPLE FEATURE FUSION PROCEDURE} identify the possible misŽ ring cylinder(s). The technique

involves a multiple feature fusion process, which is based _{4.1 Principles of fuzzy pattern recognition} on the feature level fusion architecture for multisensor

fusion [20] but with some modiŽ cation. The problem of fuzzy pattern recognition can be simply described as follows [21]: given K known patterns, As illustrated in Fig. 3, not multisensors but only a

A₁,A₂, ..,A_K, and one new pattern, B, identify which by seven features together,I(n)_F,I_H(n),I(n)_L,I(n)_S ,I(n)_C,I(n)_V and I(n)_A . This is achieved by fuzzy pattern recognition with known pattern the new pattern should be classiŽ ed into.

In this description, each pattern, denoted byA, is a fuzzy the following procedure:

vector _{1. The seven features of each individual cylinder are}

A=(a₁,a₂, ...,a_M) (17) associated together as a vector:

where each element of the vector,a_m, satisŽ es U(n)=(u(n)₁ ,u(n)₂ ,u₃(n),u(n)₄ ,u(n)₅ ,u(n)₆ ,u(n)₇ )

0å a_må 1, m=1, 2, ...,M (18) ₌(I(n)_F ,I(n)_H ,I(n)_L ,I(n)_S ,I(n)_C ,I(n)_V ,I(n)_A) (24) The fuzzy vectorAcan be interpreted as a fuzzy set in 2. U(n) is transformed into a fuzzy vector

the domainU=[u₁,u₂, ...,u_M}

B(n)=(b(n)₁ ,b(n)₂ ,b(n)₃ ,b(n)₄ ,b(n)₅ ,b(n)₆ ,b(n)₇ ) A=

G

1,

a₂ u₂, ...,

a_M

u_M

H

where the transformation of a_m to u_m is often termed

fuzziŽ cation [22], which depends on a membership _b(n)

m =í(u(n)m ) function

a_m=í(u_m) (20)

Once all of the known patterns and the new pattern have

been represented as fuzzy vectors, the pattern recog- ₌

G

m <dm 1

2+ 1 2sin

C

ð

c_m­ d_m

×

A

BD

(25) nition can be achieved by computing and comparing the

degree of closeness between the new fuzzy vectorBand each known fuzzy vectorA_k(k=1, 2, ...,K). If there is a known vectorA_j withjµ{1, 2, ...,K}satisfying

wherec_mandd_mare both constant and can be deter-ó(B,A)= max

1¢k¢M(B,Ak) (21) mined by the relationship ofu(n)_m among Ncylinders: then B is the nearest to A_j among all of the known _c

m=₁max¢_n¢_N(u(n)m) patterns, that is to say the new pattern B should be

classiŽ ed into the known pattern A_j. This is called the _d m=13c_m

nearest selection criterion in fuzzy pattern recognition. ₍₂₆₎

In equation (21), ó is called the degree of closeness

3. The degree of closeness ó₁ (or ó₂) is calculated between two fuzzy vectors [21]. Although there are many

between the new fuzzy vector B(n) and a standard deŽ nitions for the degree of closeness, each of them is

known fuzzy vector A. This standard vector A is generally intended for a particular purpose. Here two

deŽ ned under a healthy engine condition with absol-deŽ nitions are used for engine misŽ re detection:

ute cylinder-to-cylinder uniformity. Under such a 1. Maximum–minimum degree of closeness ó_{1 condition, all of the seven features,I(n)}

F, I(n)H,I(n)L,I(n)S ,

I(n)_C,I(n)_V andI(n)_A , should theoretically be unity for all of the N cylinders, and their fuzziŽ ed values should ó₁(A,B)=

æM

m=₁min(am,bm) æM

m=₁

max(a_m,b_m)

(22) _{still be unity. Therefore, the standard vectorAof all} cylinders can have the form

A=(1, 1, 1, 1, 1, 1, 1) (27)

2. Euclidean distance degree of closenessó₂

4. The following rule identiŽ es whether thenth cylinder is healthy or misŽ ring, where ó₀ is a dimensionless ó₂(A,B)=1­

S

m=₁(am,bm)

2 (23)

where A=(a₁,a₂, ...,a

M) and B=(b1,b2, ...,b_M) are two fuzzy vectors.

4.2 MisŽ re detection by multiple feature fusion with fuzzy pattern recognition

As depicted in Fig. 2, if the engine structural parameters are unknown, whether an individual cylinder is healthy

threshold and may be statistically determined from experimental data.

Rule 5

IFó_1" ó₀(or ó_2" ó₀)

THEN thenth cylinder is healthy ELSE thenth cylinder is misŽ ring

5 EXPERIMENTAL RESULTS AND DISCUSSION

5.1 Measured signals from a production engine

To obtain instantaneous angular velocity signals to vali- _{Fig. 5 Measured instantaneous angular velocity without} mis-date the proposed on-line misŽ re detection technique, an _{Ž re for mean engine speeds of (a) 700, (b) 1000,} engine test facility was set up. The speciŽ cation of the _{(c) 1200 and (d) 1500 r/min}

test engine, a model 4135D four-cylinder four-stroke diesel engine, produced by Shanghai Diesel Works and used in light commercial vehicles, is given in Table 1. The engine was loaded with a hydraulic dynamometer and was appropriately instrumented to record the operating parameters. To allow the proposed technique to be validated over a wide range of engine operation conditions, the measurement of instantaneous angular velocity was performed over a selection of speed and load settings.

An eddy current displacement sensor mounted opposite the  ywheel was used to measure instantaneous angular velocity signal, and a Hall eVect device on the camshaft provided a timing reference point at the top dead centre (TDC ) of cylinder 1. This device had the characteristic that the angular velocity resolution decreases as the engine speed increases. A personal com-puter (PC ) mounted with a Real Time Devices AD3110

Fig. 6 Measured instantaneous angular velocity with cylinder analogue-to-digital conversion data acquisition (DAQ )

3 misŽ ring for mean engine speeds of (a) 700, (b) 1000, board was used for data collection and analysis. As the _{(c) 1200 and (d) 1500 r/min}

 ywheel had 128 teeth and the AD3110 DAQ board

provided a timer counter of 8 MHz clock rate, the mini- _{5.2 MisŽ re detection capability by each individual} mum angular velocity resolution was 0.6 r/min at the _feature

highest engine speed of 1500 r/min. This resolution is,

however, considered suYcient for misŽ re detection, since _{Figure 9 shows the calculated featuresR}

TandRFfor the the angular velocity variation observed was more than _{range of operating conditions as described in Figs 5 to} 20 r/min even with the engine running in a healthy 8. It is clear that the calculated values of these two fea-condition under very low load. tures for a healthy engine are almost 10 times as great Figures 5 to 8 present waveforms of instantaneous as those for a faulty engine. Therefore, the features R_T angular velocity measured under the same load of and R_F can easily detect whether misŽ re exits in the 30 N m over a range of operating conditions (i.e. without engine, although, as previously explained, neither can misŽ ring, with cylinder 3 misŽ ring, with cylinders 2 and identify which cylinder is misŽ ring. It is also observed 3 spatially misŽ ring, and with cylinders 3 and 4 sequen- that the in uence of the engine speed, especially higher tially misŽ ring). Each Ž gure includes four plots corre- speeds, should be considered carefully when using the sponding to mean engine speeds of 700, 1000, 1200 and feature R_F, but this caution is not necessary for the 1500 r/min. Two cycles of sampled data are depicted in featureR_T.

1500 r/min under the same range of conditions as described in Figs 5 to 8. It is observed that all these features have the capability of both detecting engine mis-Ž re and locating its position. Among the eight features I(n)_T is observed to be more accurate for identifying the misŽ ring cylinder(s) than the other seven features, but its computation is more complex since it requires knowl-edge of engine structural parameters. Some features, par-ticularly I(n)_C, I(n)_V and I(n)_A, which are directly extracted from the angular velocity waveform, could not be calcu-lated under certain engine conditions. This occurs when there is no obvious acceleration in the angular velocity waveform and especially at high engine speeds or a cer-tain cylinder is misŽ ring. As shown in Fig. 11, these fea-tures are Ž xed at zero in such cases, but this simple adjustment may possibly give an erroneous diagnosis.

It is interesting to note that the diagnostic conclusions Fig. 7 Measured instantaneous angular velocity with cylin- _{implied by diVerent single features do not always concur} ders 2 and 3 spatially misŽ ring for mean engine speeds _{and sometimes they directly con ict with one another.} of (a) 700, (b) 1000, (c) 1200 and (d) 1500 r/min _{For example, the feature I(n)}

A would give an erroneous diagnostic decision with the engine at 1500 r/min when cylinders 3 and 4 both misŽ re (shown in Fig. 11), whereas other features can detect this fault correctly. This indicates that the information provided by multiple features is usually redundant and complementary, but sometimes contradictory, and one single feature may hence simply not be suYcient to make a reliable misŽ re decision.

5.3 MisŽ re detection capability by multiple feature fusion

Since the forcing of incomputable features to be zero increases the probability of an erroneous diagnosis, a feature selection process can be performed before the multiple feature fusion procedure described in sec-tion 4.2. This can be achieved by excluding the incom-Fig. 8 Measured instantaneous angular velocity with cylin- _{putable features from the feature vector shown in}

ders 3 and 4 sequentially misŽ ring for mean engine _{equation (24). For example, if three featuresI(n)}

C,I(n)V and speeds of (a) 700, (b) 1000, (c) 1200 and (d) 1500 r/min _I(n)

A are incomputable, the fuzzy vector of thenth cylinder

Fig. 10 Calculated featuresI(n)_T,I(n)_F,I(n)_H, I(n)_L, I(n)_S , I(n)_C,I(n)_V andI(n)_A at a speed of 1000 r/min (×, without misŽ re;# , with cylinder 3 misŽ ring; , with cylinders 2 and 3 misŽ ring;%, with cylinders 3 and 4 misŽ ring)

Fig. 11 Calculated featuresI(n)_T,I(n)_F,I(n)_H, I(n)_L, I(n)_S , I(n)_C,I(n)_V andI(n)_A at a speed of 1500 r/min (×, without misŽ re;# , with cylinder 3 misŽ ring; , with cylinders 2 and 3 misŽ ring;%, with cylinders 3 and 4 misŽ ring)

would beB(n)=(í[I_(n)F ],í[I_(n)H ],í[I_(n)L ],í[I_(n)S ]), which con- and the standard vectorAwill identify whether thenth cylinder is misŽ ring.

tains only four elements. Meanwhile, the standard vector

Fig. 12 Calculated degrees of closenessó₁andó₂at speeds of 1000 and 1500 r/min (×, without misŽ re;# , with cylinder 3 misŽ ring; , with cylinders 2 and 3 misŽ ring;%, with cylinders 3 and 4 misŽ ring)

at 1000 and 1500 r/min and under the same range of engine cycle, which is, for instance, 80 ms with the four-stroke engine at 1500 r/min. From this point of view, the conditions as described in Figs 5 to 8. It is observed that

all these values are less than 0.5 for a misŽ ring cylinder proposed algorithms are veriŽ ed to be fast in compu-tation and have the potential capability for on-line but more than 0.8 for a healthy cylinder. This diVerence

is so distinct that the selection of a threshold for ó₁or monitoring and real-time diagnosis of engine misŽ re. ó₂ is much more straightforward than for a single

feature.

6 SUMMARY AND CONCLUSIONS

It is also noted that the proposed multiple feature fusion technique exploits the redundant and

complemen-tary information of all the single features and thus leads In this paper, a technique for the on-line detection of engine misŽ re based on multiple feature fusion has been to improved diagnostic reliability. For example, the

pro-posed technique can identify the misŽ ring cylinders 3 proposed. Ten dimensionless features with fast compu-tational algorithms have been deŽ ned and if all these and 4 correctly with the engine at 1500 r/min. This is

important because such a conclusion is obtained when features are associated together they can Ž rstly identify reliably whether the engine is healthy or misŽ ring and the individual feature I(n)_A gives an erroneous diagnosis

(shown in Fig. 11). A similar case can be seen when the secondly locate the position of a misŽ ring cylinder or cylinders.

engine ran at 1500 r/min with cylinder 3 misŽ ring.

As described in Fig. 2, only after a data block of Although all of the single features can be used to detect misŽ re, none of these features is found to be uni-instantaneous angular velocity within one engine cycle

is available will the PC system start to analyse the data, versally successful because of the complex nature of the in-cylinder process. The diagnostic results from single calculate the features and, Ž nally, draw a conclusion on

whether the engine is healthy and which cylinder is mis- features are not always concurrent and sometimes actually con ict with one another.

Ž ring. This indicates that the proposed technique for

engine misŽ re detection is on a cycle-by-cycle basis. In The fusion of multiple features has been demonstrated to provide signiŽ cant advantages over the use of single this study, without knowledge of the engine structural

parameters, the total computation time during one features. In this way it exploits the redundant and comp-lementary information of all the features and thus leads engine cycle is 5.7 ms when using a PC system with an

Intel Pentium 10 MHz CPU and 32M RAM running to improved diagnostic reliability.

The proposed multiple feature technique has been under Microsoft Windows 95. Obviously this

com-for monitoring the condition of military vehicle engines. putation, and it may hence provide a basis for a practical

Proc.Instn Mech.Engrs, 1986,200(D1), 45–51.

utility in on-line monitoring and real-time diagnosis of

9 Rezeka, S. F. and Henein, N. A. A diagnostic technique engine misŽ re.

for the identiŽ cation of misŽ ring cylinder(s). SAE paper Owing to the limitation that the maximum speed of

870546, 1987.

the test engine is only 1500 r/min, further work is still to _{10 Citron, S. J., O’Higgins, J. E.andChen, L. Y.Cylinder by} be undertaken on other high speed engines so that the _{cylinder engine pressure and pressure torque waveform} proposed technique will also be eVective in high speed _{determination utilizing speed  uctuations. SAE paper}

conditions. _{890486, 1989.}

11 Mauer, G. F.On-line cylinder fault diagnostics for internal combustion engines.IEEE Trans. Ind. Electronics, 1990, 37(3), 221–226.

ACKNOWLEDGEMENT

12 Rizzoni, G.andConnolly, F. T. Estimation of IC engine torque from measurement of crankshaft angular position. This research was supported by the National Key Project _{SAE paper 932410, 1993.}

of China (PD9521908). 13 Shiao, Y.andMoskwa, J. J.MisŽ re detection and cylinder pressure reconstruction for SI engines. SAE paper 940144, 1994.

14 Connolly, F. T. andYagle, A. E.Modelling and identiŽ

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